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Keysight Technologies
Measuring Stress-Strain Curves
for Shale Rock by Dynamic
Instrumented Indentation
Application Note
Abstract
Three samples of shale rock, two from the Eagle Ford play, and one
from the Haynesville play, were successfully tested by instrumented
indentation. Results were remarkably repeatable, and hardness and
Young's modulus were independent of force for test forces above
300mN. For the two samples from the Eagle Ford play, the reduced
moduli were 54.3GPa and 40.6GPa, and the hardness values were
1.55GPa and 1.12GPa. For the Haynesville sample, the modulus was
22.5GPa and the hardness was 0.51GPa. By assuming a Poisson's
ratio of 0.25 and negligible work hardening, stress-strain curves
were deduced from these indentation measurements. Finite-element
simulations of indentation experiments were conducted wherein
the simulated materials were assigned the deduced stress-strain
curves. Simulated force-displacement curves matched experimental
force-displacement curves reasonably well, thus lending credibility
to the material model and to the indentation method of determining
constitutive properties.
Introduction
Shale formations host vast natural gas of plasticity. For isotropic materials,
and oil reserves which are accessed by elasticity is fully described by the
hydraulic fracturing. Experts in the oil Young's modulus and the Poisson's
and gas industry have analytical tools at ratio, n. For stresses above the yield
their disposal for optimizing fractures to stress, the material deforms plastically,
maximize the productivity of a well, and exhibiting large strains for relatively
these analytical tools require knowing small increases in stress. If the material
the stress-strain curve for the shale, as has a capacity for work-hardening, then
well as other mechanical properties. the stress-strain curve has a positive
slope, F, beyond the yield point. If the
The simplest elastic-plastic constitutive material has no capacity for work-
model is illustrated schematically in hardening, then the stress-strain
Figure 1 as a bi-linear stress-strain curve is flat beyond the yield point (F
curve. Materials for which this model = 0). In summary, such materials are
is appropriate experience elastic mechanically described by only four
deformation so long as the principle parameters: Young's modulus (E),
stress remains below the yield stress, Poisson's ratio (n), yield stress (Y), and
Y. The primary characterization of the hardening slope (F).
elasticity of the material is the Young's
modulus, E, which is the slope of the
stress-strain curve prior to the onset
Figure 1. Idealized bi-linear stress-strain curve which requires four material constants for
full definition: E, v, Y, F.
03 | Keysight | Measuring Stress-Strain Curves for Shale Rock by Dynamic Instrumented Indentation - Application Note
Indeed, shale is a complex composite of Thus, the purpose of an instrumented For many materials, the hardness is
clay, minerals, and organic material. Yet indentation test is to cause a controlled simply proportional to the yield stress
there are reasons to hope that at large contact during which measurements of the material, Y, with the constant of
scales, relative to the microstructure, shale are made to determine the contact proportionality being about 3 [6]:
might succumb to a simple mechanical stiffness, S, and contact area, A, so that
(8)
model like that illustrated in Figure 1, and reduced modulus, and ultimately, the
that further, instrumented indentation might Young's modulus of the test material
be used to obtain essential mechanical can be determined [3